There are described six incomplete time-reversal operators, under the action of which only one or two angular momentum projection operators change the sign. The incomplete time reversal operators, along with the conventional time-reversal one, are part of discrete generalized symmetry groups of 8th and 16th orders. These groups are Abelian for integer values of the angular momentum J, whereas for half-integer J they are non-Abelian. When the T–symmetry is reduced to one of six incomplete time reversal symmetries, it can be restored involving six types of metaparticles. The conclusion about existence of metaparticles follows from the group-theoretical analysis. Because there are six types of metaparticles corresponding to each particle in the Universe, it means that there are six possible metauniverses besides the Universe and the Antiuniverse.